Does the USS Enterprise 65 have a sister ship?

Answer 1

Technically all of the enterprise's have sister ships. Any ship of the same class would be a sister ship. The class name is the same as the first ship of said class usually. So the NX01, had a sister ship, the Columbia, even though it was an "nx" class which in the ST Universe is a bit of a misnomer, in the fact that is part of it's designation, as the NX is the experimental designation while NCC is the service designation.

The original series enterprise had many sister ships, including the Defiant, Potempkin, and Constitution among others.

Movie Enterprise, was the refit so again the same ship names would have applied.

Enterprise B, was Excelsior Class.

C was the Ambassador Class.

D was the Galaxy Class.

E was the Sovereign Class.

As for Naval ships here, the original Enterprize a sailing ship from England, the answer I believe is no.

As for U.S. Naval ships, then the answer is yes. Since none of them are "Enterprise" class vessels. Incidently I know that U.S. Naval ships are different from Star Trek, but Star Trek traditions are based uponm a mixture of United States, British, as well as other Maritime Naval Traditions. This happens to be one of them.